Residues of connections and the Chevalley-Weil formula for curves

TL;DR

This paper presents a novel proof of the Chevalley-Weil formula for curves by computing residues of a Gauss-Manin connection, providing new insights into automorphisms of Riemann surfaces.

Contribution

It introduces a residue-based proof of the Chevalley-Weil formula for automorphisms of compact Riemann surfaces, connecting geometric residues with character computations.

Findings

Residue computations yield the Chevalley-Weil formula

New proof technique links Gauss-Manin connections to automorphism characters

Enhanced understanding of automorphism actions on Riemann surfaces

Abstract

Given a finite group of automorphisms of a compact Riemann surface, the Chevalley-Weil formula computes the character valued Euler characteristic of an equivariant line bundle. The goal of this article is to give a proof by computing using residues of a Gauss-Manin connection.